Abstract
The fixed points of a closure function are known as closed sets in the corresponding generalized closure space and their complements are called open sets. We identify among the combinations of usual properties of a closure function some that are sufficient (but not necessary, as we show through counterexamples) in order to obtain that the family of open sets is a specific generalization of the notion of topology (namely, weak structure, minimal structure, generalized topology in the sense of Csaszar, supratopology, generalized topology in the sense of Lugojan M-structure). The properties of other operators associated to a closure function (interior, exterior and boundary operators) are also investigated.
Cuvinte cheie
Generalized closure space
minimal structure
generalized topology.